In the present study, a novel numerical method solving a thermoelastic diffusion problem with moving boundary is presented. Since the thermoelastic diffusion system is composed of three coupled differential equations, we propose an uncoupled numerical method to obtain an approximate numerical solution with quadratic convergence order in time and space. The error estimate in Sobolev space and order of convergence are obtained for the semi-discrete and fully discrete problem. The numerical approximation is based on the finite element method together with the Neumark’s approximation in time discretization. Finally, we will show that the results of the numerical simulation are in agreement with the numerical analysis.

在本研究中，提出了一种求解具有移动边界的热弹性扩散问题的新数值方法。由于热弹性扩散系统由三个耦合的微分方程组成，因此我们提出了一种解耦数值方法来获得时空上具有二次收敛阶的近似数值解。对于半离散和完全离散问题，获得了Sobolev空间中的误差估计和收敛阶数。数值近似基于有限元方法，以及时间离散化中的Neumark近似。最后，我们将表明数值模拟的结果与数值分析是一致的。